Pinning time statistics for vortex lines in disordered environments

Abstract

We study the pinning dynamics of magnetic flux (vortex) lines in a disordered type-II superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We compare different model implementations for the disorder in the surrounding medium: discrete, localized pinning potential wells that are either attractive and repulsive or purely attractive, and whose strengths are drawn from a Gaussian distribution; as well as continuous Gaussian random potential landscapes. We find that both schemes yield power-law distributions in the pinned phase as predicted by extreme-event statistics, yet they differ significantly in their effective scaling exponents and their short-time behavior.

Flux line relaxation kinetics following current quenches in disordered type-II superconductors

“…Bustingorry, Cugliandolo, and Domínguez studied a three-dimensional elastic line model of vortex matter by means of Langevin molecular dynamics (LMD) to identify physical aging features in two-time quantities like densitydensity autocorrelation and mean-square displacement [18,19]. The aforementioned studies utilized a random landscape representation for the distribution of disorder while we implement isolated localized pinning centers of uniform potential, two approaches that yield significantly different relaxation properties [20] and aging scaling exponents [21]. Pleimling and Täuber investigated the non-equilibrium relaxation properties of vortex matter as elastic lines by means of Monte Carlo simulations [21]; Dobramysl et al later verified these results with a different microscopic representation of the system's dynamics through LMD [22].…”

Disordered vortex matter out of equilibrium: a Langevin molecular dynamics study

“…For our implementation of the Langevin molecular dynamics method for disordered type-II superconductors [6,[13][14][15] we also require expressions for the vortex-vortex interaction as well as for the attractive pinning potential. The repulsive in-plane vortex-vortex interaction is given by…”

“…We illustrate the rich physics of interacting magnetic vortices in disordered type-II superconductors that is governed by competing energy and hence length and time scales, through various characteristic examples that address both fluctuations in non-equilibrium steady states [6,13,15] as well as complex out-of-equilibrium relaxation scenarios initiated from very different starting configurations [6,14,15]. In this brief overview, we focus on systems with comparatively weak magnetic fields and hence low vortex density, and at low temperatures.…”

“…(c) Similar results, but obtained for a continuous Gaussian disorder landscape correlated over distance ξ = b 0 with otherwise identical parameter values [13]. (b) of the figure explores the temperature dependence of the effective decay exponent α(T ); as the inset for the low-temperature regime T ≤ 10 −5 ǫ 0 b 0 /k B confirms, one indeed finds a roughly linear dependence α(T ) ≈ 0.0417 + 3340 T , albeit with an apparent non-zero intercept as T → 0[13]…”

Dynamical regimes of vortex flow in type-II superconductors with parallel twin boundaries

“…This particular implementation of the elastic line model was previously used by Dobramysl et al [46] to study relaxation and aging phenomena of flux lines in the presence of point-like and columnar disorder. Since then, it has been employed to investigate relaxation dynamics of vortex lines following magnetic field, temperature and drive quenches [47][48][49], as well as the pinning time statistics for flux lines in disordered environments [50]. We have extended this work to here address the dynamics of vortices driven parallel to the x axis, and perpendicular to two parallel planar defects that are placed either a short distance (16 pinning center radii b 0 ) apart or a large distance (160b 0 ) apart.…”